DSpace Repository

Fibonacci numbers and the golden rule applied in neural networks

Show simple item record

dc.contributor.author Luwes, N.J.
dc.contributor.other Central University of Technology Free State Bloemfontein
dc.date.accessioned 2015-09-02T10:02:24Z
dc.date.available 2015-09-02T10:02:24Z
dc.date.issued 2010
dc.date.issued 2010
dc.identifier.issn 1684498X
dc.identifier.uri http://hdl.handle.net/11462/343
dc.description Published Article en_US
dc.description.abstract In the 13th century an Italian mathematician Fibonacci, also known as Leonardo da Pisa, identified a sequence of numbers that seemed to be repeating and be residing in nature (http://en.wikipedia.org/wiki/Fibonacci) (Kalman, D. et al. 2003: 167). Later a golden ratio was encountered in nature, art and music. This ratio can be seen in the distances in simple geometric figures. It is linked to the Fibonacci numbers by dividing a bigger Fibonacci value by the one just smaller of it. This ratio seems to be settling down to a particular value of 1.618 (http://en.wikipedia.org/wiki/Fibonacci) (He, C. et al. 2002:533) (Cooper, C et al 2002:115) (Kalman, D. et al. 2003: 167) (Sendegeya, A. et al. 2007). Artificial Intelligence or neural networks is the science and engineering of using computers to understand human intelligence (Callan R. 2003:2) but humans and most things in nature abide to Fibonacci numbers and the golden ratio. Since Neural Networks uses the same algorithms as the human brain does, the aim is to experimentally proof that using Fibonacci numbers as weights, and the golden rule as a learning rate, that this might improve learning curve performance. If the performance is improved it should prove that the algorithm for neural network's do represent its nature counterpart. Two identical Neural Networks was coded in LabVIEW with the only difference being that one had random weights and the other (the adapted one) Fibonacci weights. The results were that the Fibonacci neural network had a steeper learning curve. This improved performance with the neural algorithm, under these conditions, suggests that this formula is a true representation of its natural counterpart or visa versa that if the formula is the simulation of its natural counterpart, then the weights in nature is Fibonacci values. en_US
dc.format.extent 2 476 462 bytes, 1 file
dc.format.mimetype Application/PDF
dc.language.iso en_US en_US
dc.publisher Interim : Interdisciplinary Journal: Vol 9, Issue 1: Central University of Technology Free State Bloemfontein
dc.relation.ispartofseries Interim : Interdisciplinary Journal;Vol 9, Issue 1
dc.subject Neural networks en_US
dc.subject Fibonacci numbers en_US
dc.subject Golden ratio en_US
dc.subject Artificial Intelligence en_US
dc.title Fibonacci numbers and the golden rule applied in neural networks en_US
dc.type Article en_US
dc.rights.holder Central University of Technology Free State Bloemfontein

Files in this item

This item appears in the following Collection(s)

Show simple item record

Search DSpace


My Account